Scaling refers to adjusting the functionality of software, such as a blockchain, in order to account for more people using it. Bitcoin, for example, was not meant for widespread use; as it has grown in popularity, its use has become less convenient. For context, imagine if every time you wanted to make a purchase using a credit card, you had to wait 13 minutes or more for the payment to go through. Obviously, this would affect the viability of credit cards as a method of payment. This is why scalability is a major issue with popular cryptocurrencies - some blockchains were unintentionally designed in such a way that the more people used them, the more time it took to verify and execute a cryptocurrency transaction. Increased traffic on the network also affects how much a typical user needs to pay in mining fees to verify the transaction on the blockchain in a viable amount of time. In other words, if you don't want to wait 13 minutes for a transaction to go through, you may have to pay more in fees to expedite the transaction.
Certain solutions, such as bitcoin's Lightning Network and Ethereum's Liquidity.Network project have been created in order to address this problem.